The objective of this research proposal is to further the development of rapid, rigorous calculations of binding affinities. The long-term goal is to provide techniques suitable for virtual screening of compounds for drug design. Existing rigorous methods for binding affinity calculations require long simulation and thus are not feasible for virtual screening. The proposed methods will calculate equilibrium binding affinities from non-equilibrium computer simulations for a range of molecular and protein systems. The aims are: (i) Develop practical guidelines for optimal use of standard non-equilibrium methods, along with a careful comparison between non-equilibrium and equilibrium methods; (ii) Extend non-equilibrium extrapolation techniques to protein-ligand systems, building on work by Zuckerman, Woolf and the applicant. These approaches overcome poor convergence properties of standard non-equilibrium calculations; {iii) Extend the single-simulation path sampling method to include molecular, then protein-ligand, systems within the TINKER software package. Developed by the applicant and Zuckerman, the method employs path-sampling to efficiently compute non-equilibrium-based affinity estimates.